Stand straight with your heels, back, and head against a wall. Bend forward from your waist, keeping your heels and bottom against the wall, to touch your toes. Can you do this without toppling over? Explain why and what you need to do to be able to touch your toes without losing your balance. Is it easier for a woman to do this? A round pencil lying on its side as in Figure 4 is in neutral equilibrium relative to displacements perpendicular to its length.
What is its stability relative to displacements parallel to its length? Suppose a horse leans against a wall as in Figure Calculate the force exerted on the wall assuming that force is horizontal while using the data in the schematic representation of the situation. Note that the force exerted on the wall is equal in magnitude and opposite in direction to the force exerted on the horse, keeping it in equilibrium.
The total mass of the horse and rider is kg. Take the data to be accurate to three digits. Two children of mass 20 kg and 30 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3 m, at what distance from the pivot point is the small child sitting in order to maintain the balance? Note that the force exerted by the wall is horizontal. A person carries a plank of wood 2 m long with one hand pushing down on it at one end with a force F 1 and the other hand holding it up at 50 cm from the end of the plank with force F 2.
If the plank has a mass of 20 kg and its center of gravity is at the middle of the plank, what are the magnitudes of the forces F 1 and F 2? The wall is in stable equilibrium without the bracing but can pivot at its base. Calculate the force exerted by each of the 10 braces if a strong wind exerts a horizontal force of N on each square meter of the wall. Assume that the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths.
Neglect the thickness of the wall. Suppose the weight of the drawbridge in Figure 12 is supported entirely by its hinges and the opposite shore, so that its cables are slack. The mass of the bridge is kg. Figure A small drawbridge, showing the forces on the hinges F , its weight w , and the tension in its wires T.
Suppose a kg car is on the bridge in Figure 13 with its center of mass halfway between the hinges and the cable attachments. The bridge is supported by the cables and hinges only. A sandwich board advertising sign is constructed as shown in Figure A gymnast is attempting to perform splits. From the information given in Figure 15, calculate the magnitude and direction of the force exerted on each foot by the floor. A gymnast performs full split. The center of gravity and the various distances from it are shown.
Skip to main content. Statics and Torque. Search for:. Stability Learning Objectives By the end of this section, you will be able to: State the types of equilibrium. For example, a marble on a saddle is stable for displacements toward the front or back of the saddle and unstable for displacements to the side.
When we consider how far a system in stable equilibrium can be displaced before it becomes unstable, we find that some systems in stable equilibrium are more stable than others. The critical point is reached when the cg is no longer above the base of support. This control is a central nervous system function that is developed when we learn to hold our bodies erect as infants.
For increased stability while standing, the feet should be spread apart, giving a larger base of support. A cane, a crutch, or a walker increases the stability of the user, even more as the base of support widens.
Usually, the cg of a female is lower closer to the ground than a male. Young children have their center of gravity between their shoulders, which increases the challenge of learning to walk. Animals such as chickens have easier systems to control. Not all birds are like chickens, of course. Some birds, such as the flamingo, have balance systems that are almost as sophisticated as that of humans. Hence, the chicken is in very stable equilibrium, since a relatively large displacement is needed to render it unstable.
The body of the chicken is supported from above by the hips and acts as a pendulum between the hips. Therefore, the chicken is stable for front-to-back displacements as well as for side-to-side displacements. When a system in equilibrium is displaced and the resulting net force pushes the object even further away from the equilibrium position then it must have been in an unstable equilibrium.
Technically, real systems cannot spend time at unstable equilibrium point because the tiniest vibration will cause them to move out of equilibrium not to mention that you could never place them perfectly into position in the first place. Trying to balance a marble on a hill is a good example:. Some structures that are in stable equilibrium and can be displaced relatively far before they are no longer in equilibrium. Other structures structures that only require a small displacement to move out of equilibrium like toddlers.
We often call these systems stable and unstable, but this can be misleading because any standing structure is somewhat stable and a truly unstable structure would not stand still for any time. These structures that are in a stable region, but could be pushed passed a tipping point are known to be in a metastable equilibrium.
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